Asymmetric Information, Debt Capacity, And Capital Structure *

Transcription

1 Asymmetric Information, Debt Capacity, And Capital Structure Michael. emmon University of Utah Jaime F. Zender University of Colorado Boulder Current Draft: September 20, 2011 Preliminary and Incomplete Do Not Quote without Author s Permission emmon: (801) finmll@business.utah.edu; Zender: (303) jaime.zender@colorado.edu We would like to thank Matthias Kahl, Chris each, Michael Roberts, Iulian Obreja, Chris Yung, and seminar participants at eorgetown for helpful discussions.

2 Asymmetric Information and Capital Structure Abstract: We present a tradeoff theory of capital structure in which asymmetric information is the sole friction. By considering both the amount of debt as well as the restrictiveness of the associated debt covenants a more complete characterization of debt structure is examined than is considered in the standard tax/bankruptcy cost tradeoff model. The leverage choice, the restrictiveness of associated debt covenants, and the renegotiation of covenants are examined and empirical implications are developed.

3 The standard tradeoff theory considers the allocation of cash flow across debt and equity securities to be the primary impact of capital structure choice and examines the implications of this allocation for taxes, bankruptcy costs, decision making incentives, information transmission, or other frictions. We develop a model of capital structure choice that considers both the allocation of cash flow and control rights in determining the firm s ideal debt structure. The model develops a tradeoff theory of capital structure in which costs associated with asymmetric information between the firm and external investors are the sole friction. A firm with uncertain cash flows and asymmetric information between the firm and the market concerning the distribution of the cash flows is examined. A capital constrained entrepreneur seeks financing from an inferiorly informed capital market. Once the firm is established a public signal concerning the strength of the industry or the economy is observed. Based on this signal, the firm may choose to either continue, generating an uncertain future cash flow, or to liquidate, for an immediate certain value. When the firm is initially capitalized, the use of debt financing is beneficial given the asymmetric information between the firm and investors. The use of debt, however, generates the standard risk shifting incentives on the part of equityholders. The subsequent need to make a continuation versus liquidation decision implies that debt covenants, which delegate the right to make this decision, may add value. Debt covenants allocate control of the liquidation decision to the firm or the lender based on the signal of the strength of the public signal. Because the lender has inferior information relative to the entrepreneur, in some states the use of restrictive covenants may entail a

4 cost. The balance of this cost and the benefit of initially issuing debt generates the tradeoff in the capital structure choice. The model is an extension of Myers and Majluf s (1984) classic model. Myers and Majluf have demonstrated that the sale of a security with low information sensitivity (debt) is motivated by the presence of asymmetric information at the time of financing. This model considers the implications of the fact that the informational asymmetry extends to a future decision point. The presence of debt alters the decision making incentives of the insider. This distortion in incentives creates an environment n which debt covenants, which transfer control rights to the lender on a state contingent basis, may be valuable additions to debt contracts. The lender s inferior information, however, implies this transfer of control may be costly. As will be shown, the optimality of the use of restrictive covenants is closely tied to the firm s ability to renegotiate these covenants when they restrict the firm from taking efficient actions. A tension between the implications of asymmetric information at the two dates develops and the two consequences of the informational asymmetry in the model allow us to derive an optimal amount of leverage for a firm. Covenants are standard features of debt contracts. They take a variety of forms and may restrict firms from taking certain actions (engaging in mergers, the payment of dividends, issuing debt) that transfer wealth from lenders to shareholders or may proscribe certain conditions the firm must maintain (minimum levels of net worth or interest coverage). The covenants modeled here are proscriptive covenants which act as an early warning system for the deterioration of the financial health of the firm and/or future default (e.g. Townsend (1979)). The presence, nature, and restrictiveness of 2

5 such covenants have an important impact on the value of debt contracts. For example, Asquith, ertner, and Scharfstein (1994) found technical covenant violation to be the leading reason for default (slightly ahead of a missed debt payment) in their sample of 76 Junk-Bond issuers. Their absence from the standard capital structure discussion therefore may be an important omission. By presenting a model in which the amount of debt as well as the structure of its control rights are considered in the leverage decision we hope to further understand the role of debt covenants and to shed light on the broader capital structure question. arleanu and Zwiebel (2009) (see also Sridhar and Magee (1997)) point out that examining debt covenants is an interesting and important example of the broader discussion of the property rights literature developed in rossman and Hart (1986) and Hart and Moore (1990). arleanu and Zwiebel develop a model that shows how restrictive covenants which allocate control of decisions to a party with inferior information may enhance value. Our model differs from theirs in that while arleanu and Zwiebel take the amount of debt and managerial incentives as exogenously given. These constructs become endogenous when we address the ex ante capital structure decision allowing a more complete consideration of the contracting problem. An optimal debt structure is chosen considering the amount of debt as well as the nature of the associated covenants. While it is not our main focus we provide an alternative to arleanu and Zwiebel s explanation for the use of restrictive covenants. Interestingly, we show that an important consideration in determining the restrictiveness of debt covenants is the firm s ability to renegotiate the covenants when they prevent efficient actions from being pursued. 3

6 One perspective on the nature of our results is that the model develops an endogenous measure of debt capacity that complements the pecking order of financing discussed by Myers (1984). An alternative perspective is that a more complete recognition of the impact of asymmetric information on the choice of financing identifies a balancing cost of debt financing under asymmetric information, placing the analysis back in a traditional tradeoff framework. The model provides a relatively conservative amount of debt as the optimum. The main issues influencing the use of debt in the model are the firm s liquidation value and the nature of the informational asymmetry. Debt levels are appropriately compared to the level of guaranteed cash flow (liquidation value in the model) given the market s information. As liquidation value is dependent upon the state of the overall economy we immediately obtain the empirical implication that firms will tend to use more debt in economic expansions than in contractions. The model derives other interesting empirical predictions concerning leverage choice, the nature of covenants associated with the firm s debt, and the costs of renegotiating such covenants. Empirically, the main capital structure implications in the model can be examined either by directly considering the impact of proxies for the initial asymmetry of information, the information concerning the quality of the firm that may be used in state contingent financial contracts (debt covenants), liquidation value, and the nature of the uncertain cash flows on leverage choice. Alternatively, this issue may be examined by considering the response of market participants to the informational limitations, the change in the nature and the restrictiveness of debt covenants as leverage changes. Ongoing research pursues both paths. 4

7 1. The Model with a Binary Public Signal In this model, an entrepreneur/manager seeks funding for a firm. The entrepreneur s type or quality is assumed to be known precisely and privately by the entrepreneur (we will alternatively discuss an entrepreneur s type or the type of firm run by the entrepreneur, good entrepreneurs run good firms etc.). External investors (the market) know only that type is drawn from a distribution F(t); where F(t) is defined on the interval [B, ], with 0 < B <, and F(t) has a well defined mean, E(t). Entrepreneurs with types in this interval are assumed to be observationally equivalent to the external market. For simplicity, we assume there are only two types and that types are drawn from the set {B, } where the ex ante probability of a good (type ) entrepreneur is θ. Initial capital, I, is required to initiate an investment project and establish a firm. The realized value of the investment project, its time 2 payoff, is assumed to depend upon the entrepreneur s type and the value of a signal w that is publicly observable (and verifiable) at time 1, where the signal, w [ w, w] has a distribution H(w). In this section, we consider the case of a binary signal where, {, }, the prob(w = w 1 ) = p, and w 1 w2 0 > >. The realized signal can be considered an ex post indication of the strength of the overall economy or the industry (where w 1 is termed a strong market and w 2 a weak market) as it will affect the fortunes of all observationally equivalent firms. The expected signal pw1+ (1 p) w2serves as an ex ante measure of expected economic conditions. If the project is funded and continues until time 2 it generates a cash flow of H or where H > > 0. The high cash flow H (success) is generated at time 2 with probability given by the product of the entrepreneur s type and the realization of the 5

8 public signal, Prob(cash flow = H type = t and signal = w) = tw, and the low cash flow (failure) is realized with the complementary probability, 1 tw. For internal consistency we assume 1> w1 > Bw2 > 0. The random variables t and w are assumed to be independent for simplicity. An alternative, available at time 1, to continuing the project is that it may be liquidated (or quit ). iquidation of any firm generates a time 1 cash flow of Q with certainty. 1 The timing of the model is such that the liquidation decision is made knowing the realization of the public signal w. Because w is verifiable it can also be used as the basis for a debt covenant which allocates control of the time 1 liquidation decision. In this sense we model the inclusion of a proscriptive covenant that requires, for example the maintenance of certain accounting ratios, failure to satisfy the requirements results in default on the debt contract. The structure of the model implies that if the lender is allocated the liquidation decision (equivalently, is given the right to call the loan), he will be making this decision based on inferior information. Initially we will assume that renegotiation of this covenant is not possible (renegotiation is infinitely costly). We then consider the nature and impact of renegotiation. In the model the entrepreneur/manager owns the rights to the project but has no capital. The required capital, I, must be raised by issuing some combination of equity and debt. More precisely, the entrepreneur chooses the face value of debt, F, the level of the public signal below which control of the liquidation decision is transferred to the lender, w, and the proportion of the firm s equity to be sold externally, α, in order to 1 Firms may be liquidated either as a going concern or piece-meal. To the extent that it is more likely to be liquidated as a going concern in a strong economy the level of Q will be related to the business cycle and is not likely to be constant across time. This is not an issue in our static version of the model, however, it will influence the empirical predictions derived from the model. 6

9 maximize the informed value of his/her retained equity, (1 α). Note that this is equivalent to assuming that the entrepreneur acts in the interest of shareholders (given his/her superior information). 2 Intuitively, the effect of this assumption is to generate an agency problem, one that increases with the amount of debt financing used by the firm. The asymmetric information at the time of financing motivates the use of debt and the resulting agency problem, which may be imperfectly controlled by the debt covenant, provides cost of debt financing at the time of the liquidation decision. The First Best We begin by examining the first best decision making within the model. The time 0 informed (assuming knowledge of the entrepreneur s type) value of the firm can be written (using an indicator variable for continuation φ(w) which takes the value 1 if the realized signal w w and zero otherwise) as: I V = E {( twh + (1 tw) ) ϕ( w) + Q(1 ϕ( w)} t w = prob( w w)( te( w w w) H + (1 te( w w w)) ) + prob( w < w) Q. Maximizing this value by choice of w, it is straight forward to find the value of the public signal below which it is efficient for a firm of a given type to be liquidated. This Q signal value is w t =. This cutoff level of the public signal has natural th ( ) properties. First, it decreases in the entrepreneur s/firm s type ( w > w ); good firms B should be continued in worse economic environments than should bad firms. Secondly, the cutoff level increases in Q ; all else equal, when liquidation is more attractive than continuing and failing the more frequently you want to liquidate firms. 2 We will leave for future work the incorporation of an optimal incentive contract in this type of a model (see for example, arleannu and Zwiebel (2008) as compared to Dybvig and Zender (1991)). We note that only the bad firm s manager need suffer from an agency problem for the development of our results. 7

10 Finally the cutoff level is decreasing in the difference between the continuation values for success (H) and failure (); all else equal, the greater is the upside potential the more often you want to allow firms to continue. In order to capture the major tensions of the more robust model but enjoy the simplicity of the model with only two levels of the public signal we will assume that in a strong economy, if w = w 1, both types of firms should continue ( w > w > w ) while in a 1 B weak market, when w = w 2, only a good firm should continue ( w > w > w ). The Agency Problem The liquidation decision of an unconstrained entrepreneur, with debt outstanding, who is operating a firm of type t is easily derived. The entrepreneur acts to maximize the informed value of his retained shares for a given face value of debt. Assuming F Q, and using the liquidation decision to maximize the informed value of equity I M M S = E {( twmax( H F,0) + (1 tw) max( F,0)) ϕ( w ) + max( Q F,0)(1 ϕ( w ))} t w t t ( ) M M M = prob( w w ) te( w w w ) max( H F,0) + (1 te( w w w )) max( F,0) t t t M + prob( w < w )max( Q F,0) t reveals that the manager of a type t firm will continue if the public signal is greater than B 2 M Q F or equal to wt ( F) = th ( F) and will liquidate the firm otherwise. Note that for any F > this value is less than w t and that the difference between wt and M w t, for a given type, increases in F; in other words the agency problem (risk seeking) introduced by the use of debt financing increases in the debt s face value. Clearly for F < (riskless debt) the manager follows the first best policy and if F Q the manager will continue regardless of the value of the public signal (equity receives a payoff only if the firm 8

11 continues and is successful). Finally, defining the agency problem to be the difference w w M t t, for a given F, the extent of the agency problem is negatively related to firm type; bad firms misbehave more than good than good. In this model, assuming the initial investment level is large enough, it will never be optimal to choose debt with a face value less than ; this is simply Myers and Majluf s result that firms use financial slack or riskless debt as the first choice for financing. Furthermore, in the absence of renegotiation, there is no benefit to using debt with a face value larger than Q. This is because issuing debt with F > Q is, at the margin, equivalent to issuing external equity (they have the same level of informational sensitivity). The motivation for issuing debt under asymmetric information is limited by the liquidation value of the firm. Finally it is useful to examine the behavior of the lender. If information is symmetric and the lender is in control of the liquidation decision they would act to maximize the value of their claim on the firm s cash flow. I D D D = E {( twmin( F, H ) + (1 tw) min( F, )) ϕ( w ) + min( F, Q)(1 ϕ( w ))} t w t t ( ) D D D = prob( w w ) te( w w w )min( F, H ) + (1 te( w w w ))min( F, ) t t t D + prob( w < w )min( F, Q). If F the lender is indifferent between continuation and liquidation. If < F Q, the lender always prefers to liquidate the firm; the limit on the upside potential of his claim causes the standard preference for certainty. Finally if F > Q it is straight forward to t show that w D t Q =. In other words, the lender has a chance to capture some of the tf ( ) upside potential of continuation; the debt effectively becomes junk debt. An informed 9

12 lender would prefer continuation to liquidation only when continuation is efficient. The lender s inferior information may give rise to inefficient decisions. Clearly, it will always be optimal for w w' w. Therefore, the structure of B the model provides us with a natural metric for discussing how restrictive are the debt covenants. A covenant written such that w' = w, labeled a nonrestrictive covenant, assigns control to the lender only in those states for which it is efficient for all types of firms to liquidate. With such a covenant no firm is inefficiently constrained and there is no scope for any firm to renegotiate to waive a covenant. There will, however, be opportunities for bad firms to renegotiate a lower debt burden in exchange for a voluntary liquidation. As w is increased from this level, the covenant becomes more restrictive until the point w' = w (the most restrictive covenant) where the lender is assigned B control in all states except those for which it is efficient for all types of firms to continue. In this case any renegotiation will entail the good firm offering to take on a larger debt burden (a higher face value) in exchange for the lender waiving the violation. For restrictive covenants on the interior of the range ( w > w' > w ), conditional on the realization of w, there may be scope for renegotiation of either type. The main result of arleanu and Zwiebel (2009) is to offer one explanation for the observed tendency for debt covenants to be written as very restrictive and often renegotiated (waived) when violated. Our analysis also points to this as a more beneficial arrangement than the alternative of writing unrestrictive covenants initially and having firms volunteer to liquidate for concessions. As is standard in pooling models, the manager of the highest type firm (type ) chooses his preferred financial structure (F, w, α) taking into account the informational B 10

13 asymmetry and its impact on the outcomes of his choices. Bad firms mimic these choices. For a good firm, the manager s decision problem can be written in terms of the expressions derived above. Furthermore we assume that the required funding is sufficiently high that the firm cannot be financed entirely with risk free debt (I > ). The Decision Problem No Renegotiation For a type firm, the manager s problem can be written as: I Max (1 α ) S ( F, w') w', F, α I I st.. α E( S ( F, w')) + E( D ( F, w')) = I t t t t For notational simplicity, we define the uninformed equity and debt values as: U I U I S ( Fw, ') = E( S( Fw, '))and D( Fw, ') = E( D( Fw, ')). t t t t The type manager selects the level of external debt (described by the face value F and a covenant transferring control of the liquidation decision to the lender for realizations of the public signal less than w ' ) and the proportion of the firm s equity α to sell externally in order to maximize the (informed) value of his retained shares, subject to the constraint that the required capital I is raised. Strictly speaking the capital constraint should be written as a weak inequality, however given that the manager of a good firm sells securities under asymmetric information it will never be optimal to raise more than is required. With the constraint written as an equality, we can solve it for the necessary level of external equity: U U S ( F, w') + D ( F, w') I (1 α) =. U S ( F, w') The constraint can then be substituted into the maximand and the manager s objective function can be written: 11

14 I U U U ( ) Obj( F, w') = S ( F, w') + D ( F, w') I S S ( F, w') ( F, w') I U S ( F, w') = ( V ( F, w') I). U S ( F, w') Where the first term, uninformed firm value less the required investment, captures the impact of inefficient decision-making and the second term captures the impact of the asymmetric information on the value of the entrepreneur s claim. In this version of the model the optimal choices, given the problem faced by the manager of a good firm, are most simply identified by comparing the value of the manager s objective function for different F and w'. By doing so we are able to illustrate the model s basic tensions. When there are only two levels of the public signal we label the choice of w' = w2 as an unrestrictive covenant and the choice w' = w1 as a restrictive covenant. A first result to note is that the value the objective function for a the manager of a good firm Obj( F, w '), with an unrestrictive covenant is larger at Q w2 BH F = ; Obj( F, w2) > Obj(, w2), where the value F = < Q 1 wb 2 F = F than at is defined to be the face value of debt at which a bad firm is indifferent between liquidation and continuation when w= w2 is observed (in other words, the highest level of risky debt at which there is no cost associated with the bad manager s incentive problem given w 2 ). This result illustrates that this model captures the standard pecking order notion that the manager is better off issuing risky debt than external equity given the asymmetric information. The qualification is that this is a general prescription on financing choice only as long as it does not alter the incentives of a bad entrepreneur by too much. If we 12

15 ignore the impact of debt financing on decision making we derive a limit on the firm s motivation to use debt financing. Proposition 1: The Pecking Order and Debt Capacity: In the absence of renegotiation, asymmetric information at the time of financing (time 0) implies that, holding liquidation decision-making constant, there is a pecking order for external financing in that the entrepreneur prefers to issue first riskless debt to the extent possible (F = ) and then risky debt to its point of informational equality with external equity (in this model, F = Q). Once this level of debt financing is reached, the entrepreneur is indifferent between issuing more debt or external equity. (Assuming the liquidation decision is made efficiently and setting F = Q provides a benchmark value for the good manager s objective function.) Proof: See the appendix From Proposition 1 we immediately see that by changing the model to include a liquidation decision a version of the debt capacity discussed by Myers (1984) is endogenously derived. At the point F = Q there is no longer any motivation derived from asymmetric information between the firm and the market to use risky debt rather than external equity. An interesting aspect of liquidation value as a ceiling for debt capacity is that this value is state contingent. During economic expansions, firms in financial distress will be more likely to be liquidated as a going concern than piece-meal. Thus liquidation value may be very near firm value, implying a high ceiling. During contractions liquidations is more likely to be piece-meal, selling the firm for the highest value of its assets in an alternative use, which can be quite low. When the costs related to the distortion of incentives from the use of debt financing and the assignment of control 13

16 rights to an inferiorly informed lender are considered, the optimal level of debt, in this simple version of the model, is below this ceiling. The innovative feature of this model is that we also consider the implications of the asymmetric information between the firm and the market at the time (time 1) of the liquidation decision (the agency problem). There are two issues to discuss. First is that the use of risky debt in the initial financing of the firm distorts the incentives of the entrepreneur/manager of both a good and bad type firm in the time 1 liquidation/continuation decision. Second is that debt covenants, state contingent changes in the control of the liquidation decision, can help to limit the cost of the distorted incentives. The use of debt covenants may not perfectly control the incentive problem because the lender prefers liquidation to continuation if the debt is risky (they have their own distorted incentives) and because the lender makes decisions based upon inferior information. The net cost of the incentive distortion associated with debt financing must be balanced against the adverse selection benefits to the initial sale of debt (rather than external equity) in determining the firm s optimal capital structure. In the model with a binary signal there are only two potential value added assignments of the ownership of the liquidation decision. The first is the use of an unrestrictive covenant. In the absence of renegotiation, this arrangement will tend to be preferred for low levels of debt (when there is little distortion to managerial decision making) as well as for high debt levels when the cost of uninformed decision making by the lender is larger than is the cost of distorted decision making by informed insiders. Because we have assumed that it is efficient for both good and bad type firms to continue in a strong market ( w 1 ) and because the lender s incentives are such that they 14

17 will always want to liquidate, it will never be efficient to allocate control of the liquidation decision to the lender in this state. Therefore, only the use of a restrictive covenant, w' = w1, leaving the manager in control of the liquidation decision in a strong market and allocating this decision to the lender in a weak market, is a second potentially optimal level of the debt covenant. With only two public signals the potentially optimal levels for the face value of debt are limited. A low level of debt ( F = F ) may be optimal if the cost of inefficient decision making is large. By choosing a low (but risky) debt level the incentives of insiders of bad firms remain efficient in the sense that they will make the right decision in both a strong and a weak market (the manager of a bad firm is just indifferent to continuation and liquidation in a bad market). The distortion of the incentives of the good firm manager is controlled by the debt covenant. For any face value of debt above F the manager of a bad firm will wish to continue for both realizations of the public signal. The manager of a good firm will also have a heightened preference for continuation; however it is efficient for good firms to continue in both weak and strong markets by assumption. If any F > F is chosen, increases in F imply no increased expected incentive costs and a strict gain from lowering the time 0 discount applied to a good firm s securities. Therefore, if F > F is chosen it will be optimal to issue debt with a face value of Q. We will label this the high debt level. Proposition 2: If the low debt level, F, is chosen, it is optimal to use a unrestrictive covenant (set w' = w2 ). This arrangement keeps control of the liquidation decision in the hands of informed insiders and the low debt level, F, ensures efficient decision making in both a weak and a strong market. 15

18 Proof: Obvious from the discussion above. Proposition 3: Assuming a high debt level is chosen, F = Q, it will be optimal to use a restrictive covenant if parameter values are such that it is efficient for an average firm, t = θ+ (1 θ) B, to liquidate in a weak market (if w t > w ). If it is efficient for a firm 2 of the average type to continue in a weak market then it is optimal to use an unrestrictive covenant. Obj( Q, w1) > Obj( Q, w2) if w t > w and Obj( Q, w1) < Obj( Q, w2) if 2 w t < w. 2 Proof: See the appendix The tensions that influence the time 0 capital structure decision are now clear. The time 0 adverse selection faced by the good type firm provides a motivation for the use of debt financing. The implied agency costs, net of any benefits derived by the use of optimal bond covenants, introduce a cost of debt. iven the lumpiness of the model with a binary public signal, we will not expect a smooth tradeoff to determine the optimum but rather expect to see parameter values for which there is a low debt optimum (F = F, when the net agency cost of debt is large relative to the adverse selection benefit) and values that indicate a high debt optimum (F = Q, when the reverse is true). The simple structure of this model with a binary public signal, however, does not allow for both possibilities. Proposition 4: In the version of the model with a binary public signal and infinitely costly renegotiation of debt covenants, it is always optimal for the good firm to choose debt with a face value of F and use an unrestrictive covenant. It is never optimal to use a high level of debt. Proof: See the appendix 16

19 There is no high debt optimum in this version of the model due to the inefficient liquidation decisions introduced by a high level of debt. The model s structure implies that the low debt optimum is a corner solution. Intuitively, one would expect that when the adverse selection benefit from issuing lots of debt (the total benefit of issuing debt with F = Q rather than F = F ) was larger than the net agency cost of the distorted incentives there would be a high debt optimum. By choosing parameter values that made the continuation decision of the bad type firm truly marginal it would seem possible to obtain high debt as the optimal solution. However in this model, what determines the importance of the bad firm s continuation versus liquidation decision important is the liquidation value, Q. When the efficiency of the liquidation of the bad firm is not important (Q is low) there is also a very small total benefit available for the use of risky debt rather than external equity in the initial financing decision. 3 The current model shows that when we extend a model of financing choice under asymmetric information to consider the incentive costs associated with the use of risky debt, a good firm s incentive to use debt is limited by the distortion to the incentives of the bad type firm. Because the firms are observationally equivalent, the market, anticipating the distorted incentives associated with large amounts of debt for a bad firm, will charge a good firm for the anticipated inefficient decision-making. This makes the use of large amounts of debt suboptimal. In this version of the model, there is a pecking order for financing choices but the point at which firm s turn to external equity (F the firm s debt capacity) is very low. In other words, this version exaggerates the impact to the Myers and Majluf conclusions of this extension to their model. 3 The continuous signal version of the model does not share this feature and so allows the development of more interesting empirical implications for capital structure choice under asymmetric information. 17

20 Renegotiation of Covenants Start by considering a good firm which has issued debt including a restrictive covenant; one which transfers control of the liquidation decision to the lender in a weak market. Within the existing model there is an intuitive renegotiation strategy that a good firm may use to separate itself from bad firms when the covenant is violated. A good firm is willing to offer to increase the time 2 payment to the lender in exchange for the lender waiving the covenant (not forcing liquidation of the firm). 4 For simplicity we will assume that the firm makes a take-it-or-leave-it offer to the lender and faces any costs in all renegotiations. This assumption gives all the bargaining power in the renegotiation to the firm and may be justified by the presence of alternative sources of financing that are available to the firm in the event a covenant is violated and the lender calls the loan. However, because the relative amounts of bargaining power possessed by the firm versus the lender in renegotiation affects our results we will discuss the impact of alternative arrangements. Due to the asymmetric information between the firm and the lender, we consider Pure Strategy Perfect Bayesian Equilibria of the renegotiation game. In this model the covenants serve to mitigate the costs of high debt levels. When renegotiation is not allowed or is infinitely costly, high debt levels, were they beneficial, would take full advantage of the low information sensitivity of debt and set the face value of debt equal to the liquidation value (F = Q). However, if a good type firm anticipates a separating renegotiation strategy in a weak market, it will not set F = Q. When F = Q there is no way for a good firm to make a restructuring offer that the bad firm will not 4 Commonly, covenants give the lender the right to call the loan. In the absence of renegotiation, if the lender is the firm s only source of financing at time 1 this would be equivalent to forcing liquidation. When renegotiation is allowed, because we have assumed the lender has access only to public information, renegotiation or refunding of the debt can be accomplished by the lender or an alternate provider of capital. For simplicity we consider that the renegotiation occurs between the firm and the existing lender. 18

21 mimic (if F = Q a manager of a bad firm receives nothing in liquidation and will therefore mimic any strategy that waives the covenant). Assume that at time 0 the manager of a good firm chooses some F R, with F < F R < Q (R indicates a high debt level associated with a restrictive covenant). Because a good firm s cash flow distribution in continuation stochastically dominates that of a bad firm there is, in a weak market, a separating restructuring offer the good firm is willing to make, F S R > F, that a bad firm will not choose to mimic (F S is high enough to satisfy a separation constraint) and that the lender will accept, believing the offer is made by a good firm. The equity value for a bad firm s manager will be higher receiving Q F R in liquidation with certainty rather than taking a small chance on H F S from continuing in a weak market. Figure 1 illustrates the possible combinations of an initial debt level with a restrictive covenant (F R ) and a separating equilibrium renegotiation offer (F S ). All combinations of F R and F S lie within the shaded triangle. Combinations on the lower edge of the shaded triangle are those for which the separation constraint binds (the bad firm is indifferent between mimicking the renegotiation offer and liquidating under the initial debt level). Note that while the good firm has all the bargaining power, satisfaction of the separation constraint implies that these offers share the efficiency gains from the renegotiation between the lender and the good firm. Proposition 5: Consider a good type firm faced with the violation of a covenant in a weak market. If the face value of debt, F R, chosen at time 0 is such that Q R > F B Q w H (1 w ) 2 2 B 1 there is a renegotiation offer 19

22 R S R ( Q F ) F ( F ) H Bw 2 which a bad firm will not mimic and the lender, believing a good firm has made the offer, will accept to waive the covenant. In the absence of renegotiation costs, the manager of a good firm is indifferent to all initial F R that satisfy the first inequality. Proof: See the appendix Interestingly, rather than there being a strict benefit to issuing debt instead of external equity, as long as the initial face value of debt chosen at time 0 satisfies the inequality given in Proposition 4, the manager of a good firm is indifferent to a set of initial debt levels that are strictly less than Q. In other words, there is no optimal F R. Intuitively, for initial levels of debt financing larger than F R the savings a good firm receives on the ex ante adverse selection problem from the use of more debt is just balanced by the cost (in the form of a higher renegotiation offer) imposed on the firm by the need to separate ex post from bad firms. 5 Simple algebra shows that there is always such a range for F R if it is strictly efficient for a good firm to continue in a weak market. We are now able to examine the full capital structure implication of the existence of a costless and fully separating renegotiation in a weak market. Interestingly, in the case of costless renegotiation, asymmetric information does not motivate an extreme use of debt financing. Rather a good firm is indifferent between low debt ( F = F ) with an R unrestrictive covenant and higher debt ( F = F ) with a restrictive covenant (anticipating the good firm will renegotiate if the covenant is violated). 5 If renegotiation is costly the manager of the good firm prefers an initial F R at the lower end of the range given in the proposition. With low initial debt, more of the ex post efficiency gains accrue to the good firm in a renegotiation (evident from Figure 1) making it more likely the gains to the firm outweigh any cost. With a binary signal the cost is either larger or smaller than the gain so optimum is not unique. When the signal becomes continuous there will be a unique optimal initial debt level. 20

23 Proposition 6: When the renegotiation of bond covenants is costless firms are indifferent to choosing high debt F R = F with a restrictive debt covenant and low debt F = F with an unrestrictive covenant. If high debt is chosen, in a weak market, good firms will renegotiate the covenant choosing F S = F while bad firms will liquidate. Proof: See the appendix. When renegotiation is costless, the separation induced by the renegotiation implies it is always optimal to include a restrictive covenant with a high debt level; rather than only for certain parameter values. Proposition 6 illustrates not only the usefulness of bond covenants in controlling the agency costs of debt but also the importance of the ability of firms to renegotiate these covenants. In the model with a binary signal, without an ability to renegotiate restrictive covenants they will not be employed. ow debt levels in combination with unrestrictive covenants are superior. If the renegotiation of covenants entails any dissipative cost, the low debt solution is a unique optimum and restrictive covenants will not be used to control the incentives associated with high debt. Propositions 5 and 6 present the results for the renegotiation of a restrictive covenant in which the good firm has all of the bargaining power and is constrained in the share of the rents that may be captured by the requirement that a bad firm not wish to mimic the good firm s offer. An alternative arrangement is for a high initial debt level, F U, to be chosen in combination with an unrestrictive covenant. In this case, renegotiation in a weak market would entail a bad firm offering to liquidate for a lower required payment. Figure 2 illustrates the nature of this type of a renegotiation. In the figure are pictured the three constraints the offer must satisfy. First, the offer, F S, must be low enough that the bad firm does at least as well with a claim to Q F S with certainty 21

24 rather than owning a small chance of H F U. Secondly, it must be that the F S is not so low that the good firm will also offer to liquidate (the separation constraint). Finally, the offer F S must be high enough that the lender, believing that a bad firm is making the offer, is willing to accept it. The area of renegotiation is represented by the shaded triangle and the lower edge of the triangle represents the bad firm s preferred offers. This is formalized in Proposition 7. Proposition 7: Assume renegotiation is costless and that a debt structure including a high debt level F U in combination with an unrestrictive covenant is in place. Then: (a) In a weak market the manager of a bad firm offers to liquidate the firm in exchange for a reduction of the debt payment from F U to F S. For any initial level of debt F U, such U w2h Bw2 ( Q ) that H > F, the manager of a bad firm offers w Bw 2 2 S ( U ) U F = Q w2 H F < F to the lender. (b) For all such U F < H, the manager of a good firm strictly prefers a debt structure of low debt, F, with an unrestrictive covenant to a high debt level, F U, with an unrestrictive covenant that will be renegotiated in a weak market by a bad firm. S U U (c) When F ( F ) = Q Bw2 ( H F ) so that the bad firm receives none of the efficiency gains in the renegotiation, then the good manager is indifferent between high debt F U with an unrestrictive covenant that is renegotiated in a weak market and low debt F with an unrestrictive covenant, for any level of Proof: See the appendix. F U > F. Proposition 7 shows that an important aspect of the decision to use restrictive or unrestrictive covenants is the identity of the party at the bargaining table in the event of 22

25 any renegotiation. In the case of the renegotiation of restrictive covenants, the separation constraint implies that the lender and the good firm share the efficiency gains from the renegotiation in a weak market. These gains increase the value of the good manager s ex ante objective function. If an unrestrictive covenant is renegotiated in a weak market, it is the bad firm that does the bargaining. To the extent that the bad firm extracts any of the efficiency gains from the renegotiation this reduces the value of the good manager s ex ante objective function. It is straightforward to show that only in the case that the bad firm renegotiates in a weak market and the lender receives all the efficiency gains in the renegotiation of the debt level does the manager of a good firm achieve an ex ante value of his retained shares that is equivalent to a choice of low debt and an unrestrictive covenant (equivalently, high debt and a restrictive covenant that is renegotiated by a good firm). However, given that the unrestrictive covenant assigns control of the liquidation decision to the (bad) firm in a weak market and the existence of alternate sources of financing it is very likely for the bad firm to have most if not all of the bargaining power in the renegotiation. This result offers an explanation for the observed use of restrictive covenants that are often renegotiated rather than a use of unrestrictive covenants with voluntary liquidation in exchange for a lower debt burden. For this reason, in the sequel we focus our attention on the use of restrictive rather than unrestrictive covenants. 2. The Model with a Continuous Signal In order to develop a richer set of predictions we extend the current model by assuming the public signal w has a uniform ( w U[ w, w] ) rather than a Bernoulli 23

26 distribution. Other than this change, the model in this section is identical to that used above. This apparently simple change increases the complexity of the representations to such an extent that we must resort to numerical solutions of the optimization problem. However, the added richness allows the development of cases in which it is strictly optimal for firms to use high levels of debt (even in the absence of renegotiation) and so develop more interesting capital structure implications. No Renegotiation The representation of the problem becomes more complex when we assume that the public signal has a continuous distribution. We first present the informed equity and debt values and then discuss the change to the problem. Using the same notation as I above, S ( F, w '), the informed value of the equity for a firm of type t, is given by: t I M M S ( F, w') = prob( w max( w ( F), w'))( te( w w max( w ( F), w'))( H F)) t t t M + prob( w < max( w ( F), w'))( Q F). Assuming that the public signal is uniformly distributed this becomes: M M I w max( wb ( F), w') max( wb ( F), w') + w SB ( F, w') = B ( H F) w w 2 M max( wb ( F), w') w + Q F w w I w w' w' + w w' w S ( F, w') = ( H F) + ( Q F). w w 2 w w t ( ). Similarly, the assumption of a uniform public signal implies that the informed values of debt are given by: 24

27 M M I w max( wb ( F), w') max( wb ( F), w') + w DB ( F, w') = B ( F ) w w 2 M max( wb ( F), w') w + ( F ) +. w w I w w' w' + w w' w D ( F, w') = ( F ) + ( F ) +. w w 2 w w U I I Finally, the uninformed values are simply S ( F, w') = θs ( F, w') + (1 θ) S ( F, w') and U I I D ( F, w') = θd ( F, w') + (1 θ) D ( F, w'). B The equations for the informed security values indicate that a complication introduced by the use of a continuous signal is the question of whether, for a given F, the covenant is optimally set at a level of the public signal that is greater or less than the level at which a bad type manager benefits more from liquidating the firm than continuing. M The relationship between w and w ( F) again limits the search to two candidate optima. B B If the covenant is optimally set so that M w' < w B the covenant does not effectively constrain the bad manager in his liquidation decision. Any covenant set so that M w' < w ( F) will inefficiently constrain good managers but not affect the decision making B of bad managers. Therefore, only w' = w, an unrestrictive covenant, can be optimal. If an unrestrictive covenant is chosen it will also be the case that F is optimally set at a relatively low level. The optimal choice of F now involves a smooth tradeoff. Fixing w' = w, as F rises above in the time 0 financing decision, a good firm benefits from selling an informationally insensitive security. However, the good firm faces a cost from the bad firm s distorted incentives, an inefficiency the good firm will pay for in the price it receives for its securities. We again label the candidate low debt solution F. 25

28 On the other hand, if it is optimal for the covenant to constrain the manager of a bad firm, M w' w B, the same covenant will necessarily constrain the manager of a good firm. iven that the liquidation decision for both types of firms is controlled by the (same) covenant, there is no additional cost derived from the incentive distortion induced by a high debt level. Assuming no renegotiation, the choice of debt that maximizes the time 0 benefit of selling (informationally insensitive) debt rather than external equity is to set F = Q. Analytically, it is straightforward to show that if F = Q, then it is optimal to set the covenant so that control is transferred to the lender for levels of the public signal that are less than the level at which a firm of the average type (the lender s information on type) would optimally liquidate, Q w' = = w t ( H ) t where t = θ+ (1 θ) B. While it is clear that only two time 0 choices for debt structure are possibly optimal, F = F w = w and (, ' ) F = Q w = w t, to date we have been unable to derive (, ' ) the analytical value of F and provide an tractable comparison of the value of the good manager s objective function under these debt structures as a function of the underlying parameter values. In what follows, we derive the value F and compare the value of the good manager s objective function at the candidate solutions numerically. Figures 3 5 demonstrate the nature of the solutions to the good manager s optimization problem when the public signal is assumed to be uniformly distributed. Figure 3a compares the value of the good manager s objective function at the candidate solutions for a given set of parameter values. Immediately apparent is the result that with a continuous public signal both the debt structure that includes a low debt level and a weak covenant F = F w = w and the debt structure that includes a high (, ' ) 26

29 debt level and a restrictive covenant F = Q w = w t are optimal solutions to the good (, ' ) manager s problem under different parameter values. In the figure the vertical axis represents the value of the objective function while the horizontal axis represents different values for Q the firm s liquidation value, holding H,, and other basic parameters constant. The black curve charts the value of the objective function under the high debt solution for different liquidation values of the firm, Q, while the grey curve charts the objective function value at the low debt solution. For low values of Q there is little total benefit to selling informationally insensitive securities available at time 0 while the incentive based costs (inefficient liquidation for both good and bad firms) of the high debt solution remain. The low debt solution is characterized by the good manager capturing some of the benefit to selling informationally insensitive securities with minimal incentive costs. Therefore, for low values of Q the low debt solution is the optimum. As the liquidation value rises, the relation between the solutions reverses. As shown in Figure 3b, the low level of debt, F, rises very slowly with increases in the liquidation value. This implies that the value of the objective function under the low debt solution will also change relatively little for increases in Q. As Q rises, the total benefit available for issuing debt rather than external equity rises. The cost of distortions in the liquidation decision making by the bad manager also rise while the cost of inefficiently constraining the good manager falls. With a continuous public signal these costs may be managed more effectively (using w' = w ) than they are with a binary signal. Therefore, the value of the good manager s t 27